Advertisements
Advertisements
प्रश्न
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Advertisements
उत्तर
Let the points be A(a, b + c), B(b, c + a) and C(c, a + b)
Area of the triangle = `1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]`
= `1/2["a"("c" + "a") + "b"("a" + "b") + "c"("b" + "c") - "b"("b" + "c") + "c"("c" + "a") + "a"("a" + "b")]`
= `1/2["ac" + "a"^2 + "ab" + "b"^2 + "bc" + "c"^2 - ("b"^2 + "bc" + "c"^2 + "ac" + "a"^2 + "ab")]`
= `1/2 xx 0`
= 0
Since the area of a triangle is 0.
∴ The given points are collinear.
APPEARS IN
संबंधित प्रश्न
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?
Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0
Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m
The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
How much paper of each shade is needed to make a kite given in the following figure, in which ABCD is a square with diagonal 44 cm.
